Neutrosophic Beta Distribution with Properties and Applications

Abstract

This research is an extension of classical statistics distribution theory as the theory did notdeal with the problems having ambiguity, impreciseness, or indeterminacy. An important life-timedistribution called Beta distribution from classical statistics is proposed by considering theindeterminate environment and named the new proposed distribution as neutrosophic betadistribution. Various distributional properties like mean, variance, moment generating function, r-thmoment order statistics that includes smallest order statistics, largest order statistics, joint orderstatistics, and median order statistics are derived. The parameters of the proposed distribution areestimated via maximum likelihood method. Proposed distribution is applied on two real data setsand goodness of fit is assessed through AIC and BIC criteria’s. The estimates of the proposeddistribution suggested a better fit than the classical form of Beta distribution and recommended to usewhen the data in the interval form follows a Beta distribution and have some sort of indeterminacy